Ok Plato some explanations would be appreciated, and why it doesn't fit with the result in my book?

It is not at all clear what you are asking.
If the question is, "Select four items from thirty of which exactly twenty are defective. What is the probability that not all four are defective nor all four are non-defective"
The probabillity that all are defective is .

The probabillity that all are non-defective is .

Now note that those two are disjoint events.

The probabillity that all are defective OR all are non-defective is .

The probabillity that not all are defective and not all are non-defective is .

It is not at all clear what you are asking.
If the question is, "Select four items from thirty of which exactly twenty are defective. What is the probability that not all four are defective nor all four are non-defective"
The probabillity that all are defective is .

The probabillity that all are non-defective is .

Now note that those two are disjoint events.

The probabillity that all are defective OR all are non-defective is .

The probabillity that not all are defective and not all are non-defective is .

Mate the question is exactly how you said. Your answer still not fitting the given result but I trust you. Thanks

Plato one more question.
As I mentioned I tried to find it using where and which is quite close to your result. Is it ok finding it like this?

Unless the trials, the events, are independent the binomial formula is not applicable.
Selecting four objects from thirty is in no way independent.

But say we have batch twenty black balls and ten white balls.
We pick a random ball from that collection. Record its color and return it to the batch.
We do that four times. Those outcomes are independent.